This document has nls (non-linear least squares) regression fits using the log-normal functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. stand age relationships. This functional form is commonly used in growth analyses, and permits a flexible shape to fit to data in an intermediate maximum (i.e., “hump” shaped) relationship. We use the sum of tree biomass growth increment method for the plot biomass growth (\(G\)) calculation (see supplementary methods). Models are fitted separately by US ecoprovince.
Hypothetically, the entire functional form of the following non-linear model is considered: \(G = (1 + (yr-1990) \cdot ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(StdAge_{t1}\) is the FIA-estimated stand age at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(G\), \(c\): the \(StdAge_{t1}\) value at peak \(G\), and \(d\): the curve shape parameter.
Data have increasing variance in \(G\) with increasing \(StdAge_{t1}\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}\) in equal-sample sized plot biomass bins (n=20) for each ecoprovince.
Model selection is used to determine. to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine the best model form either including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. For the first model selection the following models are considered:
model 1: simple model \(G = (1 + (yr-1990) \cdot ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)
model 2: phi model \(G = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)
model 3: phi-alpha model \(G = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)
NOTE:
This document contains all \(G\) observations that meet our plot based filtering criteria:
Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):
case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)
These data set cleaning criteria resulted in the exclusion of 1677 observations.
Below the model fitting procedure is implemented by ecoprovince:
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6818 5262.8
## 2 6817 5259.1 1 3.714 4.8147 0.02825 *
## 3 6816 4966.7 1 292.458 401.3532 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 25359.00
## 2 2 25356.19
## 3 3 24967.80
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.287459 0.163111 1.762 0.0781 .
## phi 0.010450 0.004348 2.404 0.0163 *
## alpha 0.642950 0.030062 21.388 <2e-16 ***
## a -6.708801 17.637541 -0.380 0.7037
## b 10.122087 17.627165 0.574 0.5658
## c 29.515767 1.965151 15.020 <2e-16 ***
## d 5.023528 4.707128 1.067 0.2859
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8536 on 6816 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 8.269e-06
## (2 observations deleted due to missingness)
## Warning: Removed 233 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 236 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 62 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18837 17004
## 2 18832 16934 5 70.65 15.713 1.805e-15 ***
## 3 18831 15835 1 1098.67 1306.545 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 67134.93
## 2 2 67048.33
## 3 3 65786.65
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.805126 0.140548 5.728 1.03e-08 ***
## phi 0.026560 0.002942 9.027 < 2e-16 ***
## alpha 0.826561 0.021000 39.361 < 2e-16 ***
## a 1.184607 0.196870 6.017 1.81e-09 ***
## b 1.437877 0.186302 7.718 1.24e-14 ***
## c 19.812728 0.783480 25.288 < 2e-16 ***
## d 1.896925 0.213805 8.872 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.917 on 18831 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 8.329e-06
## (48 observations deleted due to missingness)
## Warning: Removed 699 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 750 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 162 row(s) containing missing values (geom_path).
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 31775.02
## 3 3 NA
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.345701 0.094706 -14.209 <2e-16 ***
## phi 0.002627 0.004904 0.536 0.5922
## a 4.878560 0.119267 40.905 <2e-16 ***
## b 0.761089 0.329370 2.311 0.0209 *
## c 25.244861 1.446941 17.447 <2e-16 ***
## d -0.144102 0.070933 -2.032 0.0422 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.113 on 7315 degrees of freedom
##
## Number of iterations to convergence: 22
## Achieved convergence tolerance: 5.566e-06
## (8 observations deleted due to missingness)
## Warning: Removed 246 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 248 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 100 row(s) containing missing values (geom_path).
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_222$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_222.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8900 10536
## 2 8899 10518 1 18.627 15.760 7.247e-05 ***
## 3 8895 10278 4 240.169 51.965 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 36721.56
## 2 2 36707.80
## 3 3 36494.55
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.309507 0.094562 -13.848 < 2e-16 ***
## phi -0.024412 0.005859 -4.167 3.12e-05 ***
## alpha 0.603657 0.040209 15.013 < 2e-16 ***
## a 2.605154 0.694499 3.751 0.000177 ***
## b 2.313894 0.681731 3.394 0.000691 ***
## c 27.311405 1.976096 13.821 < 2e-16 ***
## d 1.620595 0.379452 4.271 1.97e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.075 on 8895 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 3.635e-06
## (12 observations deleted due to missingness)
## Warning: Removed 4 rows containing missing values (geom_point).
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13361 37545
## 2 13360 37529 1 16.0 5.6833 0.01714 *
## 3 13359 34363 1 3165.8 1230.7557 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 72453.54
## 2 2 72449.86
## 3 3 71273.92
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.69766 0.09287 -7.512 6.17e-14 ***
## phi -0.01632 0.00481 -3.393 0.000693 ***
## alpha 0.89405 0.02300 38.877 < 2e-16 ***
## a 3.90919 0.26051 15.006 < 2e-16 ***
## b 4.08267 0.24109 16.934 < 2e-16 ***
## c 18.00850 0.44007 40.922 < 2e-16 ***
## d 1.23768 0.08322 14.872 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.604 on 13359 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 5.066e-06
## (35 observations deleted due to missingness)
## Warning: Removed 455 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 480 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 79 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13136 38463
## 2 13135 38460 1 2.41 0.8233 0.3642
## 3 13134 35348 1 3112.72 1156.5800 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 70023.05
## 2 2 70024.23
## 3 3 68917.18
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.433522 0.115029 -3.769 0.000165 ***
## phi -0.010223 0.005051 -2.024 0.042995 *
## alpha 0.872259 0.022753 38.337 < 2e-16 ***
## a 4.054684 0.137969 29.388 < 2e-16 ***
## b 3.131202 0.136903 22.872 < 2e-16 ***
## c 16.381538 0.414907 39.482 < 2e-16 ***
## d 0.881226 0.048681 18.102 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.641 on 13134 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.873e-06
## (71 observations deleted due to missingness)
## Warning: Removed 493 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 532 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 82 row(s) containing missing values (geom_path).
## Error in nls(fg2_1, data = G_234, start = c(ge = ge.start, a = a.start, :
## singular gradient
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1320 4762.7
## 2 1319 4576.0 1 186.65 53.798 3.865e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 NA
## 2 2 7288.969
## 3 3 7237.959
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.331021 1.277561 1.042 0.29767
## phi 0.008008 0.026481 0.302 0.76239
## alpha 0.826641 0.101378 8.154 8.11e-16 ***
## a 3.056931 0.693416 4.409 1.13e-05 ***
## b 1.576055 0.494782 3.185 0.00148 **
## c 18.938597 3.082749 6.143 1.07e-09 ***
## d 0.808868 0.291207 2.778 0.00555 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.863 on 1319 degrees of freedom
##
## Number of iterations to convergence: 33
## Achieved convergence tolerance: 8.167e-06
## (6 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.85296, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.3992, p-value = 1.087e-05
## alternative hypothesis: two.sided
## Warning: Removed 46 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 50 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 61 row(s) containing missing values (geom_path).
## Error in nls(fg2_1, data = G_242, start = c(ge = ge.start, a = a.start, :
## singular gradient
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 78 85.971
## 2 76 72.790 2 13.18 6.8807 0.001793 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 NA
## 2 2 395.8674
## 3 3 380.5042
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.21893 2.53852 0.086 0.93150
## phi 0.03892 0.05628 0.692 0.49134
## alpha 0.90881 0.29409 3.090 0.00279 **
## a 6.02581 3.06663 1.965 0.05307 .
## b -4.25479 2.51536 -1.692 0.09483 .
## c 38.76418 1.45405 26.660 < 2e-16 ***
## d 0.11831 0.05408 2.188 0.03176 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9787 on 76 degrees of freedom
##
## Number of iterations to convergence: 25
## Achieved convergence tolerance: 8.7e-06
## (4 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.98592, p-value = 0.5037
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = 1.4496, p-value = 0.1472
## alternative hypothesis: two.sided
## Warning: Removed 1 rows containing missing values (geom_point).
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1805 1761.3
## 2 1804 1759.4 1 1.9299 1.9789 0.1597
## 3 1803 1741.8 1 17.6581 18.2789 2.008e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6948.424
## 2 2 6948.440
## 3 3 6932.183
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.27353 0.33952 -0.806 0.421
## phi 0.01316 0.01092 1.205 0.228
## alpha 0.42364 0.09491 4.464 8.56e-06 ***
## a -0.52751 6.93253 -0.076 0.939
## b 3.74176 6.93382 0.540 0.590
## c 26.97146 5.94271 4.539 6.04e-06 ***
## d 3.61151 4.02790 0.897 0.370
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9829 on 1803 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 6.948e-06
## (9 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91385, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -9.8187, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Warning: Removed 7 rows containing missing values (geom_point).
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_263$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_263.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_313.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_315.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Error in nls(fg2_1, data = G_322, start = c(ge = ge.start, a = a.start, :
## missing or negative weights not allowed
## Error in nls(fg2_2, data = G_322, start = c(ge = ge.start, phi = phi.start, :
## missing or negative weights not allowed
## Error in nls(fg2_3, data = G_322, start = c(ge = ge.start, phi = phi.start, :
## missing or negative weights not allowed
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_322.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_342.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6739 4646.2
## 2 6738 4626.6 1 19.59 28.533 9.515e-08 ***
## 3 6737 4305.1 1 321.53 503.155 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 24227.13
## 2 2 24200.63
## 3 3 23716.87
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.839453 0.191191 4.391 1.15e-05 ***
## phi 0.017716 0.004021 4.406 1.07e-05 ***
## alpha 0.637818 0.026454 24.111 < 2e-16 ***
## a 2.454269 0.124784 19.668 < 2e-16 ***
## b 0.706016 0.082147 8.595 < 2e-16 ***
## c 27.906459 1.761889 15.839 < 2e-16 ***
## d 0.939334 0.155412 6.044 1.58e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7994 on 6737 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 4.749e-06
## (2 observations deleted due to missingness)
## Warning: Removed 247 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 249 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 101 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8426 17788
## 2 8425 17756 1 31.86 15.118 0.0001018 ***
## 3 8424 17410 1 346.23 167.530 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 41529.83
## 2 2 41516.71
## 3 3 41352.69
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.919201 0.118686 -7.745 1.07e-14 ***
## phi -0.022794 0.006449 -3.535 0.000411 ***
## alpha 0.785104 0.057628 13.624 < 2e-16 ***
## a 3.546943 0.544737 6.511 7.88e-11 ***
## b 2.666305 0.482445 5.527 3.36e-08 ***
## c 22.383920 1.986010 11.271 < 2e-16 ***
## d 1.409723 0.295997 4.763 1.94e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.438 on 8424 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.011e-06
## (1 observation deleted due to missingness)
## Warning: Removed 280 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 280 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 58 row(s) containing missing values (geom_path).
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 3577.901
## 2 2 NA
## 3 3 3546.760
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.69640 1.44772 1.863 0.0629 .
## phi -0.03398 0.02232 -1.522 0.1283
## alpha 0.88836 0.14021 6.336 3.76e-10 ***
## a 1.62042 0.32551 4.978 7.73e-07 ***
## b 1.18139 0.33243 3.554 0.0004 ***
## c 27.82096 2.51612 11.057 < 2e-16 ***
## d -0.50622 0.11971 -4.229 2.59e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.124 on 882 degrees of freedom
##
## Number of iterations to convergence: 33
## Achieved convergence tolerance: 8.237e-06
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.97086, p-value = 2.421e-12
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.2847, p-value = 0.02233
## alternative hypothesis: two.sided
## Warning: Removed 23 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 23 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 21 row(s) containing missing values (geom_path).
## Error in nls(fg2_1, data = G_M231, start = c(ge = ge.start, a = a.start, :
## number of iterations exceeded maximum of 50
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_M231$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M231.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3322 9820.3
## 2 3317 9330.6 5 489.69 34.817 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 NA
## 2 2 17465.07
## 3 3 17280.16
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.56077 0.27311 -5.715 1.20e-08 ***
## phi -0.01051 0.01704 -0.617 0.537
## alpha 1.04948 0.07321 14.335 < 2e-16 ***
## a 5.92520 0.51987 11.398 < 2e-16 ***
## b 4.73611 0.67704 6.995 3.19e-12 ***
## c 33.08842 1.19266 27.743 < 2e-16 ***
## d 0.39861 0.04588 8.688 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.677 on 3317 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 6.321e-06
## (80 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.88609, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -13.849, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Warning: Removed 144 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 160 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 543 row(s) containing missing values (geom_path).
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1993 4061.0
## 2 1992 3841.0 1 219.95 114.0694 < 2.2e-16 ***
## 3 1983 3700.5 9 140.49 8.3651 2.464e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 9377.060
## 2 2 9267.803
## 3 3 9164.998
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.57872 0.29513 -5.349 9.85e-08 ***
## phi 0.18599 0.01376 13.516 < 2e-16 ***
## alpha 0.79954 0.08748 9.140 < 2e-16 ***
## a 3.80300 1.12004 3.395 0.000699 ***
## b 4.30989 1.10875 3.887 0.000105 ***
## c 33.42758 7.29476 4.582 4.88e-06 ***
## d 1.75074 0.51733 3.384 0.000728 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.366 on 1983 degrees of freedom
##
## Number of iterations to convergence: 18
## Achieved convergence tolerance: 7.259e-06
## (40 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94641, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.0268, p-value = 0.04268
## alternative hypothesis: two.sided
## Warning: Removed 6 rows containing missing values (geom_point).
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_M313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M313.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_M331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M331.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2621 2927.8
## 2 2620 2921.0 1 6.83 6.1259 0.01338 *
## 3 2610 2716.8 10 204.15 19.6125 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 9126.760
## 2 2 9122.627
## 3 3 8914.997
##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b *
## exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.77373 0.44346 -1.745 0.08114 .
## phi 0.03730 0.01613 2.313 0.02080 *
## alpha 0.84336 0.05298 15.918 < 2e-16 ***
## a 0.54605 1.16983 0.467 0.64070
## b 2.23565 1.19591 1.869 0.06168 .
## c 56.99643 4.61322 12.355 < 2e-16 ***
## d 2.14750 0.78713 2.728 0.00641 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.02 on 2610 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 5.3e-06
## (64 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.87747, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.8087, p-value = 9.852e-12
## alternative hypothesis: two.sided
## Warning: Removed 107 rows containing non-finite values (stat_summary_bin).
## Warning: Removed 119 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 193 row(s) containing missing values (geom_path).
## Error in nls(fg2_1, data = G_M333, start = c(ge = ge.start, a = a.start, :
## singular gradient
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_M333$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M333.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Warning in log(STDAGE_t1/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in nls(fg2_2, data = G_M334, start = c(ge = ge.start, phi = phi.start, :
## singular gradient
## Error in nls(fg2_3, data = G_M334, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA
## Warning in min(AIC1_M334$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M334.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 3 |
| 212 | Laurentian Mixed Forest | 3 |
| 221 | Eastern Broadleaf Forest | 2 |
| 222 | Midwest Broadleaf Forest | NA |
| 223 | Central Interior Broadleaf Forest | 3 |
| 231 | Southeastern Mixed Forest | 3 |
| 232 | Outer Coastal Plain Mixed Forest | 3 |
| 234 | Lower Mississippi Riverine Forest | 3 |
| 242 | Pacific Lowland Mixed Forest | 3 |
| 251 | Prairie Parkland (Temperate) | 3 |
| 255 | Prairie Parkland (Subtropical) | NA |
| 261 | California Coastal Chaparral Forest and Shrub | NA |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | NA |
| 313 | Colorado Plateau Semi-Desert | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | NA |
| 332 | Great Plains Steppe | NA |
| 341 | Intermountain Semi-Desert and Desert | NA |
| 342 | Intermountain Semi-Desert | NA |
| 411 | Everglades | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 3 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 3 |
| M223 | Ozark Broadleaf Forest Meadow | 3 |
| M231 | Ouachita Mixed Forest | NA |
| M242 | Cascade Mixed Forest | 3 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 3 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 3 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | NA |
| M334 | Black Hills Coniferous Forest | NA |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | NA |
| Code | Ecoregion | region | n.obs | n.plots | ge | ge.2.5 | ge.97.5 | phi | phi.2.5 | phi.97.5 | alpha | alpha.2.5 | alpha.97.5 | a | a.2.5 | a.97.5 | b | b.2.5 | b.97.5 | c | c.2.5 | c.97.5 | d | d.2.5 | d.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6825 | 2859 | 0.2874589 | -0.0322888 | 0.6072066 | 0.0104502 | 0.0019270 | 0.0189735 | 0.6429503 | 0.5840195 | 0.7018810 | -6.7088010 | -41.2838864 | 27.866284 | 10.1220869 | -24.4326577 | 44.6768315 | 29.51577 | 25.66346 | 33.36808 | 5.0235276 | -4.2039126 | 14.2509677 |
| 212 | Laurentian Mixed Forest | east | 18886 | 8936 | 0.8051263 | 0.5296386 | 1.0806140 | 0.0265601 | 0.0207928 | 0.0323274 | 0.8265606 | 0.7853994 | 0.8677219 | 1.1846067 | 0.7987248 | 1.570489 | 1.4378769 | 1.0727087 | 1.8030450 | 19.81273 | 18.27704 | 21.34842 | 1.8969248 | 1.4778470 | 2.3160026 |
| 221 | Eastern Broadleaf Forest | east | 7329 | 3559 | -1.3457005 | -1.5313516 | -1.1600494 | 0.0026268 | -0.0069870 | 0.0122406 | NA | NA | NA | 4.8785600 | 4.6447631 | 5.112357 | 0.7610893 | 0.1154287 | 1.4067499 | 25.24486 | 22.40844 | 28.08128 | -0.1441024 | -0.2831518 | -0.0050530 |
| 222 | Midwest Broadleaf Forest | east | 4923 | 2431 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 223 | Central Interior Broadleaf Forest | east | 8914 | 3781 | -1.3095074 | -1.4948708 | -1.1241440 | -0.0244119 | -0.0358968 | -0.0129271 | 0.6036573 | 0.5248380 | 0.6824765 | 2.6051538 | 1.2437763 | 3.966531 | 2.3138939 | 0.9775443 | 3.6502435 | 27.31140 | 23.43780 | 31.18501 | 1.6205945 | 0.8767802 | 2.3644088 |
| 231 | Southeastern Mixed Forest | east | 13401 | 6113 | -0.6976600 | -0.8796939 | -0.5156262 | -0.0163198 | -0.0257474 | -0.0068922 | 0.8940459 | 0.8489688 | 0.9391230 | 3.9091946 | 3.3985539 | 4.419835 | 4.0826651 | 3.6100997 | 4.5552306 | 18.00850 | 17.14590 | 18.87110 | 1.2376798 | 1.0745533 | 1.4008063 |
| 232 | Outer Coastal Plain Mixed Forest | east | 13212 | 6392 | -0.4335225 | -0.6589964 | -0.2080486 | -0.0102231 | -0.0201239 | -0.0003223 | 0.8722590 | 0.8276606 | 0.9168573 | 4.0546841 | 3.7842445 | 4.325124 | 3.1312016 | 2.8628523 | 3.3995509 | 16.38154 | 15.56826 | 17.19482 | 0.8812257 | 0.7858048 | 0.9766467 |
| 234 | Lower Mississippi Riverine Forest | east | 1332 | 744 | 1.3310210 | -1.1752514 | 3.8372934 | 0.0080081 | -0.0439415 | 0.0599576 | 0.8266407 | 0.6277610 | 1.0255203 | 3.0569307 | 1.6966130 | 4.417248 | 1.5760551 | 0.6054087 | 2.5467015 | 18.93860 | 12.89097 | 24.98622 | 0.8088683 | 0.2375887 | 1.3801478 |
| 242 | Pacific Lowland Mixed Forest | pacific | 87 | 87 | 0.2189324 | -4.8369759 | 5.2748406 | 0.0389228 | -0.0731777 | 0.1510232 | 0.9088109 | 0.3230842 | 1.4945376 | 6.0258092 | -0.0819196 | 12.133538 | -4.2547925 | -9.2645580 | 0.7549730 | 38.76418 | 35.86820 | 41.66017 | 0.1183081 | 0.0106045 | 0.2260116 |
| 251 | Prairie Parkland (Temperate) | east | 1819 | 819 | -0.2735319 | -0.9394195 | 0.3923556 | 0.0131621 | -0.0082566 | 0.0345808 | 0.4236413 | 0.2374933 | 0.6097892 | -0.5275078 | -14.1241533 | 13.069138 | 3.7417555 | -9.8574119 | 17.3409230 | 26.97146 | 15.31613 | 38.62679 | 3.6115127 | -4.2883307 | 11.5113561 |
| 255 | Prairie Parkland (Subtropical) | pacific | 674 | 298 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 27 | 27 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 173 | 173 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | interior west | 215 | 215 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 310 | 242 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | interior west | 195 | 106 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 341 | Intermountain Semi-Desert and Desert | interior west | 62 | 62 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 121 | 120 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 93 | 61 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6746 | 2998 | 0.8394531 | 0.4646580 | 1.2142481 | 0.0177158 | 0.0098341 | 0.0255975 | 0.6378178 | 0.5859605 | 0.6896751 | 2.4542693 | 2.2096525 | 2.698886 | 0.7060158 | 0.5449813 | 0.8670504 | 27.90646 | 24.45260 | 31.36032 | 0.9393341 | 0.6346776 | 1.2439905 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8432 | 3849 | -0.9192014 | -1.1518555 | -0.6865474 | -0.0227936 | -0.0354347 | -0.0101524 | 0.7851036 | 0.6721383 | 0.8980689 | 3.5469427 | 2.4791244 | 4.614761 | 2.6663048 | 1.7205935 | 3.6120162 | 22.38392 | 18.49085 | 26.27699 | 1.4097232 | 0.8294956 | 1.9899507 |
| M223 | Ozark Broadleaf Forest Meadow | east | 890 | 346 | 2.6963990 | -0.1449729 | 5.5377709 | -0.0339763 | -0.0777800 | 0.0098274 | 0.8883603 | 0.6131784 | 1.1635421 | 1.6204165 | 0.9815431 | 2.259290 | 1.1813938 | 0.5289410 | 1.8338467 | 27.82096 | 22.88268 | 32.75923 | -0.5062169 | -0.7411607 | -0.2712730 |
| M231 | Ouachita Mixed Forest | east | 988 | 481 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M242 | Cascade Mixed Forest | pacific | 3404 | 3384 | -1.5607736 | -2.0962569 | -1.0252903 | -0.0105068 | -0.0439108 | 0.0228972 | 1.0494784 | 0.9059351 | 1.1930217 | 5.9252007 | 4.9059108 | 6.944491 | 4.7361090 | 3.4086420 | 6.0635761 | 33.08842 | 30.75000 | 35.42683 | 0.3986055 | 0.3086487 | 0.4885623 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 2030 | 2024 | -1.5787192 | -2.1575161 | -0.9999223 | 0.1859908 | 0.1590037 | 0.2129779 | 0.7995398 | 0.6279842 | 0.9710954 | 3.8030004 | 1.6064142 | 5.999587 | 4.3098883 | 2.1354531 | 6.4843235 | 33.42758 | 19.12137 | 47.73378 | 1.7507415 | 0.7361737 | 2.7653093 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 19 | 19 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 362 | 362 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 1713 | 1713 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 2681 | 2671 | -0.7737332 | -1.6433049 | 0.0958386 | 0.0372978 | 0.0056780 | 0.0689176 | 0.8433571 | 0.7394668 | 0.9472473 | 0.5460495 | -1.7478438 | 2.839943 | 2.2356502 | -0.1093856 | 4.5806859 | 56.99643 | 47.95049 | 66.04237 | 2.1474997 | 0.6040457 | 3.6909537 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 1678 | 1678 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M334 | Black Hills Coniferous Forest | interior west | 365 | 171 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 213 | 213 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning: Removed 21 rows containing missing values (geom_point).
## Warning: Removed 21 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_hline).
## Warning: Removed 21 rows containing missing values (geom_point).
## Warning: Removed 22 rows containing missing values (geom_point).
## region weighted.ge
## 1 entire US -0.3267201
## 2 pacific -1.4113029
## 3 east -0.1863573
## 4 interior west -0.2723565
## region weighted.phi
## 1 entire US 0.0076104930
## 2 pacific 0.0574464617
## 3 east -0.0002416832
## 4 interior west 0.0131289526
## region weighted.alpha
## 1 entire US 0.6365641
## 2 pacific 0.8758168
## 3 east 0.6629378
## 4 interior west 0.2968644